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Hello, I am doing a math project and my main focus is computer graphics. I want to explore the mathematics behing interactive games, and right now I want to use free 3D models on the web and somehow code it to do an animation whenever I press a button. Ex. Space bar makes the model jump in the air. I was just wondering if OpenGL would be able to perform my this task, and if yes can you please direct me to tutorials on how to do this. Thank you.

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Yes, you can animate models with opengl (though, generally, most of the "animation" doesn't involve opengl at all, but whatever language you're coding in, opengl just renders it). A couple online resources I found helpful are here and here, though there are certainly others. Depending on whether you want to animate via key-frames, pre-animated models with bone-rigging (where you may have a jump/run/whatever animation and simply select which is animated) or whether you want interactive animation (where you rely a little more on physics and move the bone rig independently) you may need to either learn to animate in blender/maya or whatever modeling program you use, or find open-asset models that come with animations.

It's a rather involved process (I personally found it extremely difficult), however you go about it, but good luck! .